An online cross product calculator determines the cross-product for three dimensions. Our innovative vector multiplication calculator aims to simplify and streamline magnitude, direction, and normalize vectors, and spherical coordinates.

## What is Cross-Product?

**The cross product is the vector quantity that indicates both direction and magnitude and it also measures how much two vectors point in different directions.**

Our vector calculator computes the cross-product between the types of vectors.

## Formula:

The cross product calculator is a way to calculate the product of two vectors. The formula used for the calculation is as follows:

**C = a x b = |a| x |b| x sinθ x n**

Where:

- a and b are the two vectors
- θ is the angle between the vectors
- | | are the magnitude of the vectors
- n is the unit vector at right angle of both vectors

You can try our __Trapezoid area calculator__ to find the area and parameters of trapezoid shapes.

## Relation Of Cross-Product And The Right-Hand Rule:

Our right hand rule calculator is used to find the direction and magnitude of cross product vectors. It aid’s in determining the resultant vector’s direction.

The statement of the right-hand rule is as follows:

If you point your figure in the direction of the moving positive charges and your middle finger points in the direction of the magnetic field and your thumb indicates the magnetic force that pushes the moving charges.

## How To Calculate The Cross Product?

The procedure to calculate the magnitude and direction by our cross product calculator is as follows. Let's take a look at the example below.

### Example:

Let’s consider two vectors

$$ \vec u = 2\vec i – \vec j + 3\vec k $$

$$ \vec v = 5\vec i + 7\vec j – 4\vec k $$

Set up the cross product matrix

$$ \vec u \times \vec v = \begin{vmatrix} i& j& k&\\ 2& -1& 3& \\ 5& 7& -4& \end{vmatrix} $$

Finally, calculate the determinants of the metrics

$$ \vec u \times \vec v = (4 – 21)\vec i – (-8 – 15)\vec j + (14 + 5)\vec k $$

$$ \vec u \times \vec v = -17\vec i + 23\vec j + 19\vec k $$

If two vectors have the same direction or have opposite directions from each other means that they are not linearly independent. Then their cross-product is equal to zero. More generally the magnitude of the product of two perpendicular vectors is the product of their lengths.

You can also use our __standard form calculator__ to compute the numerical expressions into their standard form.

## Working of Cross Product Calculator:

The vector product calculator is loaded with a user-friendly interface that shows the cross-product of the vectors within a couple of seconds. Just stick to the given steps to find the cross product by the cross product vector calculator.

**Input:**

- Choose the vector representation ( by coordinate, by point )
- If you choose by coordinate, then you need to put the values of the coordinates
- If you select by point, then you need to put the values of the initial points
- Enter the terminal points in the designated fields
- Tap “calculate”

**Output:**

Our vector cross product calculator determines the following results:

- The cross product of two vectors
- Vector magnitude
- Normalized vector
- Spherical coordinates (radius, polar angle, azimuthal angle)
- step-by-step calculations

## FAQs:

### What Are The Uses Of The Cross-Product Calculator?

The cross-product can be used in determining the followings:

- Calculate the angle between two vectors
- Determining the vector normal to the plane
- Calculate the moment of a force about the point
- Calculate the moment of a force about the line

### Difference Between The Cross And Dot Product?

- The dot and cross products are involved in multiplying and magnitude of two vectors.
- Dot product returns the number while the cross product returns the vector
- Dot products work in any dimension, but the cross product works in the 3d dimension.

### Is Cross Product Always Scalar?

The cross product indicates the direction and magnitude so it is a vector.

### Cross Product Is Perpendicular Or Parallel?

The cross product of two vectors is always perpendicular. It is defined as the vector c that is perpendicular to the vectors a and b with directions and magnitude equal to the area of the parallelogram.

### What Are The Applications Of The Cross-Product?

It has a wide range of applications in different fields

- Investigate the moment of inertia
- Investigate the rotating objects
- Used in Physics, Engineering, Computer programming C

## References:

From the source Wikipedia: Cross product, Definition, Computing, Properties, Alternative ways to compute, Applications, As an external product, Generalizations.

From the source Khan Academy: Cross products, properties of the cross product, The right-hand rule, matrices intro, determinants.